数学物理学报(英文版) ›› 2000, Vol. 20 ›› Issue (4): 504-510.
丁晓庆
DING Xiao-Qiang
摘要：
This paper studies the value distribution of random analytic Dirichlet series
f
!(s) =
1P
n=1
Zn(!)e−sn, where {Zn} is a sequence of independent random variables,
with moments zero, such that inf
n
E{|Zn|}/E1/2{|Zn|2} > 0. Suppose [h()]2 =
1P
n=1
E{|Zn|2}e−2n converges for any > 0, and diverges for = 0. It is shown that if
lim
!+0
log+ log+ h()
log(1/) = 2 (0,1), then with probability one,
lim
!+0
n(; t0 − ", t0 + "; f
! = a)
(1/) log h()
2
27+
"
8t0 2 R, 8" > 0, 8a 2 C,
where is a constant depending only upon the constant .
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